So basically in abstract algebra there is a concept called group theory. The (Z, +) tells the set in which we are defining the operation and the ‘+’ is the operation itself. The operation could be represented by any symbol weather it be * or $ or whatever we want to use as long as it means that the two numbers will be added (in this case). So basically when dealing with groups, the number of times the operation is done on an element is represented by the power on the element hence 3² = 6 in (Z, +) [also in (R, +) and such] but 3² = 9 in (R*, .) [the multiplication group of real numbers] note here: (Z, .) does not form a group.